A letter to Professor Stewart, on the objects of general terms, and on the axiomatical laws of vision ; to which are here added, some remarks on the Monthly review on this subject

LETTER

TO

PROFESSOR STEWART,

ON THE

OBJECTS OF GENERAL TERMS,

AND ON THE

AXIOMATICAL LAWS OF VISION.

SECOND EDITION.

TO WHICH ARE HERK ADUED,

SOME REMARKS ON THE MONTHLY REVIEW ON THIS SUBJ1

J3Y J. FEARN, ESQ.

JLonuon :

1816.

ro

DUGALD STEWART, ESQ.

1 . R. SS. LOND. AND EDIN. &C. &C. &C
TORMLRLT PROFESSOR OF -MORAL PHILOSOPHY IN JIIE

university of edinburgh.

Sir,

In presenting a view of the two following subjects, each
of which has occupied the attention and urged the genius of
thinking men, to a great and celebrated extent, I am impelled by
reasons of no ordinary complexion : And, while it is to be expected
that the topic which stands Jirst subjoined, may, in the outset,
interest a more numerous class of literary persons, I am highly
urged to solicit the important issue of your earnest notice of that
one which is placed last. The former subject, however, besides
its own importance, has a certain bearing upon the latter, although
it be not obvious here.

The matter of the " Laws of Vision," to which I here attach
the greater interest, is presented as exhibiting what I (who certainly
speak under strong inducements to caution) am obliged, by the
nature of the thing, to consider a mathematical analysis of the
constituents, cr cause, o/'Visible Figure. This, I apprehend, it
must be considered ; since the Four Laws of Vision are not phy-
sical laws merely, but are also Four Axioms, whose truth
consequently is necessary, and whose nature is certainly ma-
thematical. Fully anticipating, as I do, the first impression of so
extraordinary a matter, and sensible of the utility of some sort of
passport, in my peculiar case ; may I therefore be permitted to
offer the following observations ?

When, about two years since, I ventured to publish a few copies
of the u Principles of Primary Vision" (the Jirst hint concerning
which, appeared about four years back) I had indeed a confident
hope that I should have to repeat the subject : but I did not expect

3 J Mr. Fearn on ine Axiomatical Laws of Visiwi. 233

so curious and valuable a support, as the discovery that I am com-
pletely borne out by the rigorous ssumption of an illustrious Greek
Geometer, Such, however, is an authority which, owing to a
recent communication, I am eiubled to cite, and therefore purpose
to bring forward here ; not, however, without the additional
concurrence of living individuals ; which, together, form a very
different voucher from my own very questionable judgment, as to
whether this matter is what I conceive it to be.

Valuing, as I must do, the concurrent authority of Proclus,
thus made known to me •, I rest no undue confidence cither_upon
iiis, or upon any other single voice. In the present case, indeed,
the imperative nature of the evidence looks down upon single
suffrage : but, since even mathematical propositions must bow to
collective suffrage, I derive no small resolve from being able to pledge
myself here, that among the acute and scientific individuals to
whom the matter has been personally communicated, there has oc-
curred but one dissent, (limited to inessentials) and that one has
not survived discussion. The principal value, therefore, which I
attach to the concurrence of Proclus is, that I feel no reluctance
in making an open use of it, for the advancement of the subject.

While I am naming that Geometer, it may be of material con-
sequence to state, that although the fact assumed by him attests the
truth of the Laws of Vision, yet these Laws have no dependance
whatever on that fact. But of this I must speak hereafter. May
I however add, that Proclus has not handed down his proofs ; but
that the fact itself was fallen upon by me, I need not say, without
any knowledge that another had gone before. Indeed, that this
fact, known to Proclus, was completely lost to the moderns, as
to any utility, is fully manifest from its not being noticed by
any one of those who have engaged on the great problem, to find
the nature and place of visible fgurc.

Of authorities, ancient and modern, who have asserted the
dominion of sense over the elementary objects of geometry,
there is a numerous host •, and these are of the highest estimation :
only they have cdl failed to prove their assumption by showing the
precise manner, how the elements of visible fgure are either
connected, or formed. Proclus alone (seconded by Barrow), is
partly an exception, in having noted one included or subordinate
fact ; which, however, never led him to the Four axioms ot
vision, nor to the place of perceived figure.

Such, Sir, is the prospect of this matter : while, either from the

• Sir.ce this was first printed, I have found the matter is further backed
1)Y a slight but unequivocal allusion of Dr. Bakuow, fully recognising the
tame fact lhat is assumed byPp.oci.us: although neither of these writers
deduce from it in j consequences in philosophy.

234 Mr. Feara on the Ashnptical [4

want of some such pai the foregoing, or fro:- my own culpa-

ble remissness i:i nor c g to urge the matter througl the ordinary
channel- <r in m ,1 am oblige to believe it

cannot . • reached \cur eye, or undergone the sentence of votir
judgmei Unquestionably I am bound to my contemporaries
and to tlu future race, to place this matter in the direct channel of
your notice, since the command to do so has fallen tins im-
perative I . upon me

Bes: 1 1 , -, let me tow beg to

suggest to notice, th r very remarkable .t with that

astonishing metaphysical i i*/of theHiNDoi h makes «• <JU

reaiiom rather an energy than t which" the

infinite mind, who i it at ail times, and m all placet, r.r-

hibits tu his creatures a ceptiotu, Itl 'rf /hi picture,

or piei . , akiat/s unij

I the bare mention I had almost tid, divine)

to me unavoidable ti mark, that, if it
can strictly be said mat it " took its ri ■ from I high theological
speculation," it must have been indeed k HIGH one : since the most
luminous I I modern physical re teal eh It ave but led, by a slow

and groping | rard this solar light of Hindoo Phi-

losophy.— Can any person without astonishment contemplate such
a coincidence of M ng from so very distant sources, and

flowing through such different channels?

'I he mind is rapt anil lost in attempting to conjecture at what
time, under what circums; , nd by what guidance, the early

genera tions of our species were enabled to | hy of

buch s flight, that the living spectator, of the highest cast, must
intellectual dimensions on the comparison, — a
phil lophy which teaches the moderns, at once to appreciate the

d to stop at the line where that genius
rror, — which dentin the inertness of n
without admitting such a chimera as the non-reality oi I x-
tensios. — Such is the KxTir.vAi. Would of Hindoo K
And, (so tar, therefore, as any ■ coincident* can corroborate

the sentence ol internal n , ) may I not set value upon the

fact, that this Ex ti.rnal World of THE Hindoos, is to color
and nr.uuE in is, as we supp- rnal fire to be to the

NRE i/( a bodt a7i/f/4 it heats r I indeed SOOpOM this simile is
vague ; but I nevertheless affin >, that I ri appears to be as

requisite and as close, in the former cafie as in tht latter, after wc
have gone through the following analysts of the primary phenomena
of

The seeming correlation of these two subjects, n.mely, the
HINDOO i STERNAL WORLD, and what 1 have felt obliged to call
the " axiomatical law:> or vision," is the more satisfactory,

.5] La** qf Vision. 23.5

since the rays of Hindoo Knowledge that have pervaded the
immense and hideous regions of their course to us, are ample
evidence that its pristine laboratory shined with an effulgence not
now imaginable ; and prove, that a day of science has once
passed over the earth, whose fellow is yet but dawning upon
mankind.

In fine, Sir, it cannot be unwelcome here to mark the direct
bearing of these united result-, upon all the coiulusium of Atheism !
— What a transition, from sublime admiration, to pity and debase-
ment, does the mind suffer on turning from the HLlNDOO INTER-
NAL world, to listen to the Gki ibbles concerning dead
matter ! — What a relief, to ascend back in contemplation, to
that point where the physical speculations of a Boscovich meet
the met.ipb.VMc.il tenet Of the Hindoo ! — Can it be indifferent to
the j" r, — Can it be indifferent to the CITIZEN, to inquire
whether an J/iali/sis of primary Mental Phenomena makes a
i hird CoiM< n i MT upon this high point ?

Here it remains only, that 1 have the honor to subscribe myself,

Sir,
Your most obedient servant,
Vmiom, Jufy 3 Iff, 1817. JOHN FEARN.

ader. — It being requisite, for convenience, in the
Pamphleteer, to insert in the present number only anc of the
TWO distinct subjects treated under the foregoing Letter, and the
subject placed last by the author being the OOC principally alluded
T>> in this prefatory Letter; be interest of its having been

t iken up in the Monthly Review for March last ; it becomes essen-
tial to its being clearly and duly apprehended, to insert " The
Axiomatical I liston" in the present number.

ON THE
AXIOMATIC AL LAWS 0¥ \ ISIOft

PREFACE.

The most proper preface to the following subject, on the pre-
sent occasion, appears to be that of introducing (he fact asserted by
Proclus, which has already been alluded to in the addr. ss prefixed
to this publication. In stating this fact, however, it may be of no
small consequence to note, very particularly, that although its truth

236 Mr. Fearn on the Axiomatical [6

must attest the truth of the Laws of Vision, (which is my reason for
bringing it forward here) yet if the fact could be actually disproved,
this could not at all affect these Laws, since they do not depend upon,
but include, the fact asserted by Proclus. Yet, nevertheless, I must
add, that I believe myself to have distinctly proved the fact in ques-
tion ; which, it is to be remarked, is not proved by Proclus, but
only asset ted by him.

In Mr. : lationofthe " Commentaries of Proclus on

the first booh of Euclid? l i ," Vol. I. page 125, is this pas-

cage, "We should admit the followers of Apollonius, who sav, that
we obtain the notion of a line when we are ordered to measure the
ks alone, either of ways or walls ; for then we do not subjoin
either breadth or bulk, but only make one distance the object of our
consideration. But a line may become the object of our sensation, if
we behold the divisions of lucid places from those which arc dark,
or survey the moon when dichotomised ; for this medium has no
distance with respect to latitude, but is endued with longitude, which
is extended together with the light and shadow."

'Hie perspicuity of the abov 'ion of this fact, is highly

conclusive and valuable. But 1 cannot avoid remarking, how strange
it appears that anv philosopher who had adverted to this fact in the
particular instances (tf il the divisions of lucid PLACEs//<vm
those which are dark," should not have intuitively discerned that
the principle is general, universal, and sole : which it must be,
since light and contiguous shadow, produce in us two sensa-
tions of colors, with a line between them ; just as is, and MUST
be done by any other two colors whatever. — His not discerning
the universality of the fact was the only thing that could have
kept Proclus from advancing on, to discern the Four Laws of Vi'
sion and their axiomatical nature, together with their direct conse-
quences.

OF THE EXTERNAL CAUSE OF VISION.

1 . Distant bodies are not, by any medium, the generic cause
of Vision ; since sensations of colors, accompanied by figures,
are as constantly, and as variously, excited by experiments of pres-
sure upon the eye, and by other bodily affections, as they are by
light reflected from distant objects.

This general fact being duly recognised, ascertains of itself the
independence of Vision upon external distant bodies, and removes
a very great and most pernicious stumbling-block, which has strange-
ly been suffered to remain an obstacle to all advancement, although
uniform experience has long demanded its expulsion from the sub-
ject.

1. When the optic organ is stimulated, either by light, by sen-

7] Laxvs of Vision. 237

sible pressure, by certain bodily diseases, or by any other such im-
pulse, the mind undergoes a set of sensations called colors. Such
are those beautiful phantoms that appear to us when we look at a
landscape or a rainbow. These phenomena seem to adhere to ex-
ternal distant objects, like a skin cast over them : but there is no fact
upon which philosophers are more unanimous, than that they are
nothing but our own sensations. It is therefore here assumed,
as a first principle, by universal consent, that thantoms of
colors are but " a species of thought."

3. With this only settled principle, it has ever been one of the
greatest problems in philosophy to discover the nature and place
of thosco/ttlines, that are seen as it were surrounding (lie phantoms
of colors, and to which we give the appellation of VISIBLE figure.
— There now exist only two opinions concerning this matter : Per-
ceived figures are either the real identical forms of external and
distant bodies-, or, they are actually the forms of our own sensa-
tions, which, if so, do not show, but only indicate, some unknown
external cause. The highest authorities of the last century have
divided upon this point: and the literary public, impressed by the
untoward character of the schism, appear to consider all proof, or
foundation on the subject, as a desideratum utterly hopeless.
•Such is the discouraging introduction to the following principles.

OF THE POSSIBLE CASES OF VISION.

All the possible cases, or accidents, of Primary Vision fall under
Four general Facts, ot I

Each of these Four Lavx an Axiom : Its truth docs not

depend upon the . i he, but on the law of THOUGHT ;

since, the moment it i-. apprehended, we discern that its contrary
possi A'. This combination of a mathematical nature with a
jJiysicat nature, form-, the most striking and important character of
the Phenomei a of strict Vision.

Two of the Laws of Vision are (INFORMATIVE, either of any.//-
gure, or of any element qfji.

The other two Laws -vr, either of some figure, or

of some element of figure.

FIRST LAW. -UNFORMAT1VE.

Prop. No one uniform sensation of color can ever be accom-
panied by a perception of any visible figure, any line, or any point.
/ ■ !. If the unclo.ude heaven, or if it skim the

| | \ OF ONE

color •, and here it i^ should ever

any point, so long as the sight
keep within the field of this one color.

238 Mr. Feara em the Axiomatical [»

It is plainly as impossible to conceive a visible line, without
calling up some second color, as it is'to conceive a boundary to an
infinite surface : For, any color we perceive, must be extended ab-
solutely without limit, if it be not terminated by our view of some
second color.

SECOXD LAW.— FORMATIVE.

Prop When any two unblended (i. e. unsojiened) sensations of
colors ar- felt at the same time, they must meet by their nearest
edges, and this meeting we must perceive as a line.

Inst. It the eye traverse either the firmament, or the ocean, until
it :.rrive at, and take in, any second color ; the evidence we have
for this fact can be no other than our being conscious where one sen-
sation of color ends, because the other begins. This meeting
of the two sensations of colors, is a line of contrast and o/*con-
tiguity in our view : and a perceived line, therefore, is purely
nothing but A THOUGHT OF DISCRIMINATION, which
we make between two of our own sensations. At the same time it
must be evident, upon reflection, that we can no more avoid perceiv-
ing the CONTRAST, and the EXTENDED DIRECTION of
this contrast, than we can avoid being conscious of the tiw dij-
it sensations of colors xchich form this contrast.

THIRD LAW.— FORMATIVE.

Prop. When any two unblended sensations of colors are felt at
the same time, and are so disposed as that one of them embraces or
surrounds the other, we must perceive a line of junction, which is
where the embraced sensation meets that which embraces it. Such
a line must return into itself ; and thus is formed every complete
figure th.it the visive faculty can strictly apprehend.

Inst. When we look at the Moon, surrounded by the azure sky,
we suffer a sensation of silver white, embraced by a sensation
of azure, and the line perceived between these two sensations re-
turns circularly into itself; which people take for the circle of the
Moon.

It must be an obvious truth here (although it is overlooked by
Proclus) that, WHi rr.viR be the hues or tints of the two sen-
sations employed, there can be but one UNIVERSAL principle that
gives an v perception of si line between them ; and this principle
l« A PERCEPTION OF CONTRAST.

I )URTH LAW.-IJNFORMATIVE.

Prop. When any two sensations of colors are felt at once, and arc
blended or softened at their nearest edges, they never can be per-

9] La W$ of Vi si cm . g 3 9

ccivrd as forming an m, not even if their distant

parts be of the nost ite coj vs.

Inst. T t uy surf; conceived 0 be black all round its edge,

and whit, in its centre, a: d let the two colors run r^r lualK into
each other : No line can ever be perceived from looking within the
field of this surface.

Innumerable other instances of this fact may be observed; such
as when we look at waving corn, or shot silks, spheres, mirrors, or
drinking glasses.

This Fourth Law strikingly illustrates the other three •, because
herein we suffer two sensations of colors with a negation of all
figupe, or line, between them ; and here, therefore, we are, by a
new result, more vividly (though not more certainly) convinced
that it is NOT COLOR, but CONTRAST, that is the CREA-
TIVE PRINCIPLE of any perceived visible figure, or line.

To conclude. Visible figure is a positive thing to our view,
but only a relative thing in regard to the two sensations 01
colors which combine to give it being : it is nothing but the co-
LOCAL or co-extended relation of one sensation to the other.
— To say, therefore, that we perceive visible figure, is to say that we
perceive the co-local or co-extended relation which one sensation
of color bears to another one, felt at the same time.

It follows, upon the highest kind of evidence, that visible FI-
GURE is nothing but a creature of the percipient, — a
thought of the mind, — [yd, we must infer) a thought resulting
from the action of some external cause, stimulating our visive
constitution.

Thf. Laws of Vision are Mathematical Axioms.

The four General Facts of Vision are herein called only Laxvs, be-
cause their subjects are, in the first place, sensible or natural phe-
nomena. But it must be insisted upon that they possess afar
higher title, in being mathematical axioms.

What venders this consideration most important, is, that even
could it be proved that visible lines are not mathematical as to the
property of being void of breadth, this (as lias been already remarked)
would not hinder the Laws of Vision from being Mathematical
axioms in the class of their evidence^ the self-evident neces-
sity of their truth.

Physical laws (it is agreed on all sides) are not nccrssary, in our
conception: they rule what is •, but, may not rule what shall be:
Light may fail to excite sensations of dors in the human mind ;
MM sensations of colors may, • lit we know, be excited in

minds without eyes : all this is com ivably possible. But, to con-
ceive any one sensation of color with a boundary or line to it ;

240 Mr. Fearn on the Axiomatical [10

Or, to conceive any two unsoftencd sensations of colors at once
without A line between thcmy is an impossibility of the very
same class, as to conceive an infinite surface with a limit, or two
contiguous mathematical surfaces without the line that makes them
two.

Now this perceived necessity of the Laws of Vision, is, I
must insist, a paramount test that a visible line is not an external
thing ; because, it is not merely an object of sense, but is an ob-
ject of INTUITION j and it is not merely a thing that now is,
but a thing that ever MUST BE, if its co-efficients exist,
Every external object is a thing that may not be at any future
time : and, while it exists, we know not its co-efficiefits : but, we
absolutely know the co-efficients of a visible line by the same process
of rationality, and to ihesame perfection, that we know that
the co-efficients of any idea of relation must be SOME TWO
THINGS, between which the mind ■perceives this relation.
Here I must refer to the small tract I published some time ago
upon " Necessary Connexion;" in which my object is to show
that we absolutely know the co-efficients of all our IDEAS
OF RELATION; and in which I suppose the thing is rigidly pro-
ved. Now, sensations of colors are IDEAS ; and I repeat it
here, that we have the same degree of cognizance of their rela-
tions (one to another) that we have of the relations of equal, dou-
ble) or half, between any two mathematical quantities ; that is, we
perceive the. NECESSITY of the relation, 50 long as the two
subjects ideally exist; and we intuitively perceive that the relation
cannot exist unless its two subjects ideally exist.

If this matter stand the test, what a change is thus produced in the
assumptions and scope of mathematics, to find, that its conclusions
are not limited to hypothetical or conditional truth, but embrace
also facts, and concrete existences ! What an enlargement of
the field of demonstrable subjects! And how curious, thus to find
a community of subjects between two sciences hitherto considered,
in their very essences, incompatible !

VISIBLE LINES ARE VOID OF BREADTH.

This general fact (it is always to be remembered) is wholly sub-
ordinate to the Laws of Vision, being included in those laws, but not
necessary to their truth. At the same time, however, it is a fact
rigidly demonstrable.

A mathematical line (of the schools) Is demonstrated to be void
of breadth, in consequence of its being defined to be « the common
boundary of two contiguous surfaces.''' Now, if one of the two sur-
faces be conceived by us to be blue, and the other one yellow, it is

11] Laws of Vision. 241

plain the mathematical line of 'contiguity ', and the line of contrast
of the two sensations of colors, is one same line; and since this
line has no breadth as the common boundary between the two su?°-
faces, it can have no breadth as the common boundary between the
two sensations of colors.

To attempt to invalidate this upon the ground of the imperfec-
tion of sense, would only prove that the person who undertakes it
does not apprehend all the terms of the subject. The subject is A
line that WE SEE: And, (without any appeal to the suffrage of
Proclu-) I may safely maintain that we don't see what we don't
see. The imperfection of sense only makes us not see breadth^
in some instances where breadth really is before us, and where a
magnifying power makes it evident : But the imperfection of
sense cannot make us see breadth when it makes us not see it.
In rigid truth, therefore, the imperfection of the organic process
of sense, causes the perfection of the mathematical line we SEE;
for the organ will not convey a report of breadth to the sentient,
in some cases wherein the external object that we look at really
has some minute breadth.

A visible line cannot be of any one color ; because it is proved
(by the First Law J that no one color ever can have a line. If then
a visible line have any color, it must be a part of each of two con-
tiguous colors: but this would show a double out-line to every
object, which we know to be a result utterly contradicted by the
fact. — Moreover, if any such double or two colored lines be suppo-
sed, it is plain that each one is but a rim of its own suriace; and
what is surface cannot be line; neither can two contiguous sensa-
tions of colors appear to us as forming a line until we mark the
place where BOTH COLORS CEASE TO BE, by reason of
their coming in contact.

It is true, I readily grant, that we see instances enough of breadth
in what are called softened lines, or where two colors blend: But
none of these things are visible lines; they are all visible surfaces,
and they must be stript of the appellation of lines, in an inquiry
like the present. — Visible lines I consider to be, all those lines
which are void of breadth to the naked eye, and which can farther
attest that they are breadthless to the naked eye, by showing no
breadth when subjected to a magnifying power. — Such lines, the
reader will find, are raised in our sentient by our looking at the
edges of the letters of good printing, as divided from the white
field of the paper : and such lines, too, are seen when we are look-
ing at most other objects.

It must be an obvious truth, that a visible line which shows no
breadth under a magnifying j)Ower, can have no breadth to the na-
ked eye. It is therefore vain to trv to overturn the fact, even if
VOL. XII. Pam. NO. XXIII. Q

_ H Mr. Fearn on the Axiomatical [12

we could by the strongest power produce any evidence of breadth :
for it must still remain, that the natural eye of man enables him
to see so line?, but lines that arc VOID OF BREADTH is
HIS APPREHENSION OF [HEM.

Finally ; Bat if, in the face of experiment and of common sense,
anv person choose to assert that A VISIBLE LINE HAS INVISI-
BLE BREAD III; then, (I must repeat it betel this absurd con-
tradiction in terms, if raftered to itand for an objection, could be
of no coir ■■■■ LAWS OF Y IMO\' ; for the,. Lawi must

still be AXIOMS, and a fltlBLI LINE WUUt still be nothing but
A LIMEOFCONTRAS1 bi rwiBK rwo SENSATIONS: And
the C( >N rRAST 1 INK must still, an, I f ' **«

S ENS A • • F which form it, which is in THlMIND n

HEREUPON, I make the appeal, in this one question, — Will

MfftUj thcYovR Axioms ov vision) be «ftT .illumed, that Vi-
sible Figures «r» the duiant THINOSOf .■■. sal world ?
Or, will it b- I that Pisib: ! is not a pheno-
menon of the mind f

The " Monthi.t Rf.tiew," for March last, baring done me the
honor to take up the foregoing tubic ! f « Prin-

ciples of Prim I published by mo in 1 8 1 5), it h*J become

very material to its advancement, thai I ; Did embnM
earliest opportunity, even at the disadvantage of a very short notice,
to explain some points which have appeared to demand illus-
tration.

Fir-r, however, I must ciW-T my tcstim mil Rtv

having gone into the subject, ami baring " n opinion

thereupon, in having felt himself in the

discharge of a scriou H ; I tided, and

concisely stated, (as he 1 the radical principle of the

• / rtainly, he could not I • r force

to their claim, than bv . tting befor ri th.it self-refu-

tation into which., I ■ ■•■:, Dr. Reid fell.

The subject is, by thil R l rw and other Publications, placed in a
light under which, I have at length the satisfaction to know, it
cannot be overlooked : The matter in the eye of the

public : it must therefore be either done trway by some objections
which can meet the expectation \ or else, a consequent inference
must be drawn.

It remain* now due to the matter in question and to mys'-If,
that I should speak to the " sell-meant hint" of a Critic who has
taken such high ground between the public and the subject.

?3] LdWi of Vision. 24 3

ft may he supposed I was struck by a hint, coming from a quarter
which has thus commanded mv respect, to " avoid the appearance of
quackery and puffing, which must attach, however unjust it/, to such
titles as those we allude to." Nevertheless, when I was roused to
f the thing, I quickly perceived that such an unworthy
and unreal appearance must indeed attach to it, in the eyes of
every nun of science who is hitherto a stranger to the peculiar
nature of the Mibject : And perhaps marry persons might not
add the candid conclusion, that anv charge upon this ground
would he mode M unjustli/." In this case, therefore, I trust that it
will not be unacceptable to mv honorable and manly chastiser,

re no such thougl : of an apol

nor could I feel 1 ring a mere^fststification ;

.se I shall put in a piea ot logical necessity } if not I : mall

claim on th .<■ just distinctions which (onone

hand ) separate mi; subject from ..!! the subjects ot physical evidence.
The title ol " Paramount Pi I i that

suppleni' • ■. i ,/ the principle < ?

Since th .Wished the " Principles of

I pi," in a more regulai I 1 therein I <i (med ilnect

to call these princ tull title I u / Demonstration.'1

v, In mv '•/•• /' • • Stewart" it has since app !

that I sir • the phenomena rigidly to demand the

title oi Vision." Now, it appears very

ni of the subject, that tin- attention of

•lblic should be awakened to the real and whole nature of

the tinng : and it is t!. fortunate that the exception

to M appearar .it mv " Titles" lias furnished

me an fending tl

1 t, to render justice to my Critic, I willingly advert to the two
following considerations, n mely, I ii<- Phenomena of l~i>i<>n have
Always been held to be merely physical appearances, contingent in
their existence, and but experimental in theii Upon the

other handS the term- ** A, ,' . I «« J} ration" are re-

stricted in philosophy, to necessary relations between our ,
Certainly therefore, when anv man of science is presented with the
title ot " ./ D istratinn'> prefix--.! to what he III nly a

speculation in physics, he must be disgusted : and tin- seems to have
been the effect on the R n •■ The following remarks, it is to
be h 11 completely remove, or prevent, anv such feeling

of the matter in futt.

1st. The Phenomena of Vision cor different clas-

r>, and of K

[line t .1 he sena ii « olors,

themselves, are merely conttr ristences, which i si

244 Mr. Feurn o?i the Axiomatical [14

may, or may never, exist : But, every time that ant two of them
exist together {iinsoftcne d) it is (I say) a necessary late of thought
that we must perceive the relation called a line between them.

Precisely with equal truth to the above, all the principles IN Geome-
try are only mere contingent ideas, which may, or 7nay ne\ er, exist in
any mind : But, every time that the ideas of any two triangles
equal to a third, are called up in our miml, we must perceive a
relation between the first txio, which is the relation of ec/uali/y.

In other words, I maintain that Euclid's Elements, and the Laws
of Vision, are each alike made up of two classes of thoughts :
One of which classes contains only contingent ideas ; The other
class necessary relations between those contingent id

L'dlv. A «. utfical Axiom is a simple Theorem, expressing
an ett .'. •: b 'tween any two substantive ideas. Now cacli

of the l4 1' k Law, 01 VISION*' is such a Theorem : The second
law, for instance, afTirms that a line is a necessary relation
;iy two unsoftened sensations of colors ; And our under-
stand] mi the self-evident imj>ossibility qf its ever being
other.

1 . in this very partial illustration, the discerning Critic will
perceive, that the thing I am respectfully offering for
consideration, if it be found to be any tiling at all, or that
men in general shall join with my ingenuous Critic, and others,
in openly confessing that they " cannot detect its fallacy " it must
then be quite foreign to its highest nature, to call it cither " an
hypothesis," or yet a physical subject : because, on the contrary,
it must take it> place, absolutely in mathematical scieme.

To prevent being possibly misunderstood here, 1 must reiterate the
following distinctions •, namely, Sensations of colors must ever be a
physical subject ; their existence is contingent, and their evidence
is EXPERIMENTAL. — Visiblelines mustcverbea mathematical
subject; their nature is necessary, and their evidence is DEMON*
stra tive I

It must now, I hope, appear, that in order to treat my subject at
all, it was imperative upon me toassiga to the Principles oi Vision,
the mathematical terms and " Titles" which I have done. In a
word, it was my being struck with the mathematical character of one
class of the phenomena of Vision, that alone led me to the change
which I hope is effe< ted in the subject. Bishop Berkeley had bent
his great acumen upon sensations of colors in their physical character,
that is <■/<" ideas in relation to ourselves ; But he failed in throwing
any light on the Problem of Perception, solely because he
never happened to be struck by the mathematical relations which
our ideas of colors have between each other.

One word remains to be added, as to my " style" Upon the
ground of its " awkwardness* I do, with great humility, abandon this

15] Lavs of Vision. 245

matter to the censure of the Reviewer. But I hope my above
remarks will lead him to suppose, that I could defend my « philoso-
phical language" in many instances wherein, from the nature of
the subject, it may appear very exceptionable. His .strictures there-
upon, I nevertheless receive with great respect, and a desire to keep
them in view : Sincerity and candour are eminently manifest in
them •, and I court the continuance of such correction.

In thejirst impression of the foregoing letter, I omitted to remark,
that any supposition of visible lines HAVING breadth (although refut-
ed above, and although if tenable it would be of no consequence to
the " law 1 01 vision,") is however a supposition that could only
embrace all those Visible Lines occasioned by our looking at colors
spread upon one same continuous s'trfaccy such as tbe objects on a
Painting, or a Writing. All other visible lines (which are infinite-
ly the more ordinary and more numerous i defy every pretence
to suppose that th my visible breadth; because, it is mani-
fest, for instance, that the color of my hand, when I hold it up to
the light, cannot run into the color of the sky which does not
touch my hand by several miles; and therefore such lines can have,
no breadth in themselves ,■ fai less, then, can we see in them what
they have not.

Tin, last kind of lines is what I gave for Examples, in the
original broaching of the subject : and it was quite gratuitous my
choosing to defend, as I still do, ihcjirst kind, also.